FleaStiff
FleaStiff
Joined: Oct 19, 2009
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May 12th, 2019 at 8:05:19 AM permalink
Quote: GBAM

If you mean confusion on my part I am certain I have the rules and payouts correct. We play this game a lot

Confusion on ANYONE'S part is just like drunkenness, eventually one sobers up and the windfall dries up. So I would not bank on any erroneous payout continuing.
GBAM
GBAM
Joined: Feb 26, 2019
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May 12th, 2019 at 8:06:15 AM permalink
Thatís fair haha.
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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May 12th, 2019 at 10:15:28 AM permalink
Quote: GBAM

Thank you for doing this. The highest payout for 7/7 is 200:1, not 500....

It makes quite a difference being 200/1 rather than 500/1.
2 8 50 200 = 4.490 629%
2 9 50 200 = 1.639 277%
GBAM
GBAM
Joined: Feb 26, 2019
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May 12th, 2019 at 11:25:00 AM permalink
Quote: charliepatrick

It makes quite a difference being 200/1 rather than 500/1.
2 8 50 200 = 4.490 629%
2 9 50 200 = 1.639 277%



Excellent. I wasnít sure if the 500 was a typo or if you misread. Thanks so much for doing that. Not terrible either way, but wish it was 9 : 1. Itís a fun bet to hit. Wonder what the base game is

Is it P(4flush)*2 +P(5flush)*8+P(6flush)*50*P(7flush)*200 minus P(3 or 2 or 1 flush)*1

That is odds of winning* amount - odds of losing* wager
Sorry for the bad formatting


Iíd love to be able to answer these questions myself
Mission146
Mission146
Joined: May 15, 2012
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Thanks for this post from:
kgb92
May 12th, 2019 at 1:06:00 PM permalink
Quote: GBAM

Excellent. I wasnít sure if the 500 was a typo or if you misread. Thanks so much for doing that. Not terrible either way, but wish it was 9 : 1. Itís a fun bet to hit. Wonder what the base game is

Is it P(4flush)*2 +P(5flush)*8+P(6flush)*50*P(7flush)*200 minus P(3 or 2 or 1 flush)*1

That is odds of winning* amount - odds of losing* wager
Sorry for the bad formatting

Iíd love to be able to answer these questions myself



Okay, so the first thing that you want to do is figure out the probabilities of a flush. What we are going to start with is the fact that there are:

nCr (52,7) = 133784560

There are 133,784,560 ways to arrange seven cards out of fifty-two. (You will see we multiply by four for the matches, that's because there are four suits, but the way we are doing the combinatorial part we're acting like there is only one suit and making up for it later.)

Seven Card Match:

nCr (13,7) * nCr (39,0) = 1716 * 4 = 6864/133784560 = 0.0000513063689861

Six Card Flush:

nCr (13,6) * nCr (39,1) = 66924 * 4 = 267696/133784560 = 0.002000948390457

Five Card Flush:

nCr (13,5) * nCr (39,2) = 953667*4 = 3814668/133784560 = 0.02851351456

Four Card Flush:

nCr (13,4) * nCr (39,3) = 6534385*4 = 26137540/133784560 = 0.19537037756

You may care about two and three card flushes, but I don't, because they lose just as equally. Thus, I just want to know the overall probability of losing:

1-(0.0000513063689861+0.002000948390457+0.02851351456+0.19537037756) = 0.77406385312

Cool, now we just slap in your paytable:

((0.0000513063689861 * 200) + (0.002000948390457*50) + (0.02851351456* 8) + (0.19537037756*2)) - (.77406385312) = -0.04490628819

That means a house edge of 4.490628819%.

Now, if we change that eight to one to a nine to one:

((0.0000513063689861 * 200) + (0.002000948390457*50) + (0.02851351456* 9) + (0.19537037756*2)) - (.77406385312) = -0.01639277363

We're going to trim that House Edge to 1.639277363%

I like this online calculator for combinatorics (the nCr function):

https://web2.0calc.com/

However, you could just steal the probabilities from Wizard's High Card Flush page:

https://wizardofodds.com/games/high-card-flush/

Found under the, "Flush Bet," section, which is the same bet you're talking about with a different paytable. I used that to verify what I was doing, naturally.

So, now you know how to do it yourself cleanly and now you know how to cheat to do it!
Vultures can't be choosers.
Dobrij
Dobrij
Joined: Jun 6, 2012
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May 12th, 2019 at 2:50:27 PM permalink
I apologize if I say stupidly...
...but maybe there was just a game of different levels?

: )

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